2020/10/13 by Vassilis Kalantzis, Γεώργιος Κόλλιας, Kalantzis, Vassilis +9
Computer Science · #Advanced Graph Neural Networks #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Information Retrieval (cs.IR) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Recommender Systems and Techniques
paper · pdf · doi:10.48550/arxiv.2010.06392
openalex publication_date 2020/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel in applications such as Latent Semantic Indexing and Recommender Systems. Nonetheless, the proposed framework is purely algebraic and targets general updating problems. The algorithm presented in this paper undertakes a projection view-point and focuses on building a pair of subspaces which approximate the linear span of the sought singular vectors of the updated matrix. We discuss and analyze two different choices to form the projection subspaces. Results on matrices from real applications suggest that the proposed algorithm can lead to higher accuracy, especially for the singular triplets associated with the largest modulus singular values. Several practical details and key differences with other approaches are also discussed.